A combinatorial wind field model

This report is the deliverable 2.4 in the project Distributed Control of
Large-Scale Oshore Wind Farms with the acronym Aeolus. The objective
of this deliverable is to provide an understanding of the wind eld model and
dynamic variations superimposed on the mean eld.
In this report a dynamical model is developed for the wind
ow in a wind farm based on nite volume method. Afterwards the model is transferred into a discrete framework called combinatorial, which determines the future behavior of the discrete system. In this regard, the dynamical model is de-
rived and it is explained in terms of ordinary dierential equations (ODE).
Considering some assumptions on the ow model (e.g. steadiness), the sys-
tem can be approximated by a linear n dimensional system. Partitioning
the state space into cells is performed by dening Lyapunov function sets,
such that each cell is the region between two neighboring level surfaces of
Lyapunov functions. The resulting discrete system facilitates a supervisory
approach to the control.